2007-08-24 23:46:47 UTC
The idea behind these curves is there is a small set of points, called control-points, which determine the overall shape of the curve (which contains many points). In other words, you can manipulate a few points and change the shape of a curve easily. Different curves have different properties. Some curves always pass through all the control points, some curves are "pulled" towards the control points but don't pass through them. It all depends on the mathematical properties of the curve.
> what if initial points are not explicitly given or known, but instead
> the math form of the function of the curve in certain segment of interest
The input to these curves is a set of control-points, not a function. The reason .math and .math.func are included is because they are used to parse the control-string. Purpose and examples of control-strings are found in the documentation (inside the CAPI download).
Note: the .math and .math.func are part of MESP (math expression string parser). You can use MESP to evaluate user defined functions.
